From: http://erikdemaine.org/puzzles/LCS2002/
Goal:
- have eight squares with images all facing the same way "up" (on both sides or on each side?)
- no cuts, rips tears
- one piece of paper
How many ways to fold?
Possible ways to pick squares for both sides: 16 choose 8 = 12870
Can we fold into quarters?
- Adjacent quarters with two perpendicular half folds (four ways)
- Opposite quarters folding diagonal in (clamshell?) (two ways)
No, since no quarter has all images facing up, so we probably need more folds.
Can perpendicular folds along lines between images work?
Six lines to fold along, but order matters e.g. can fold edges around.
Will the fortune teller fold work?
No, since it only folds each quarter into itself.
Can we fold off the grid / diagonally?
Yes, but opens more possibilities since we can make a square from triangles now.
Can we get one side (align four facing us)?
Yes (draw circle around center to mark it).
How can we get both sides?
Need to fold in half.
Now what?
Play with it.
Done?
Yes (all four aligned on each side at least), marked both sides.